This assignment examine your basic understanding of Arithmetic for Computers. To cover these concepts, answer the bellow questions $($Q$1-$Q$3)$:

Q$1.$ Perform the following arithmetic $($showing all the steps used$)$: $(25$ points$)$

a$)$ Multiplication : $1001$ X $0011($ unsigned integer $)[$ Note. this is equal to $9$ x $3)$

b$)$ Multiplications: $1001$ x $0011($two$$s complement integers$-$signed number$)[$ Note. this is equal to $-7$X$3]$

c$)$ Division : $10010011/1011$

d$)$ Addition : $110111+1100$

e$)$ Subtraction: $3925($in binary$).$ Remember. Subtraction in Binary is addition of the two$$s complement.

Q$2.$ Consider the following Floating$-$points in decimal: $(40$ pints$)$

a $=125$ x $10-3,$ b $=2\mathrm{.}2$ x $103,$ c $=0\mathrm{.}000625$ x $102$

a$)$ Fill the following table by computing the required floating$-$point operations.

a $+$ b b $-$ c a x b a$/$c

b$)$ Fill the following table by converting the resulting floating$-$point into binary:

a $+$ b b $-$ c a x b a$/$c

c$)$ For the following floating$-$point instruction: add.s $f$1,$ $f$2,$ $f$3.$ Assume that the values of $f$2,$ $f$3$ are $$ and $.$ What are the values $($in binary$)$ in $f$2,$ $f$3$ and $f$1$ after executing this instruction?

d$)$ Consider a floating$-$point addition instruction add.d in MIPS assembly language, specifically focusing on the registers $f$2,$ $f$4,$ and $f$6.$ The task involves adding two double$-$precision floating$-$point values stored in registers $f$4$ and $f$6,$ then storing the result in register $f$2.$

Given the following decimal values for variables a and b:

$$ a $=125\backslash$times $10-3$

$$ b $=2\mathrm{.}2\backslash$times $103$

Instructions:

$1.$ Convert the decimal values of a and b into their IEEE $754$ standard binary representation for double$-$precision floating$-$point format.

$2.$ Execute the addition operation using the instruction add.d $f$2,$ $f$4,$ $f$6,$ where:

o Register $f$4$ contains the value of a$.$

o Register $f$6$ contains the value of b$.$

$3.$ After performing the addition, provide the binary representation of the result stored in register $f$2$ according to the IEEE $754$ standard for double$-$precision floating$-$point numbers.

Q$3.$ In Floating Point representations, answer the following questions showing all the steps: $($Use the IEEE $754$ standard for all$)($showing all the steps used$)$: $(35$ points$)$

a$)$ Write down the binary representation of the decimal number $31\mathrm{.}625$

b$)$ Write down the binary representation of the decimal number $31\mathrm{.}625$ assuming the IEEE $754$ double precision format.

c$)$ Write down the binary representation of the decimal number $45\mathrm{.}45.$

d$)$ Write down the binary representation of the decimal number $-19\mathrm{.}625.$

e$)$ What decimal number does the bit pattern $0\backslash$times $0$C$000000$ represent if it is a floating$-$point number?

f$)$ What number is represented by the following single precision float $($single Precision$)$ : $11000000101000..\mathrm{.}0000$

g$)$ What number is represented by the following single precision float $($single Precision$)$ :$11000001110000000000$